705 views

### Why is $\sqrt{4} = 2$ and Not $\pm 2$? [duplicate]

I've always been told that if $\ x^2 = 4,$ $=>x = \pm2$ But recently, Prof. mentioned that if $x = \sqrt{4}$, Then $x = +2(only)$ I am very skeptical about this because they both mean the ...
23k views

### Is sqrt(x) a function? Does it matter if a domain is given? [duplicate]

Possible Duplicates: Reason why the even root of a number always positive Square roots — positive and negative I saw the following during a practice exam: $f(x) = \sqrt x$ for $x ≥ 2$ ...
654 views

### Why does Wolfram Alpha say that $\sqrt{1}=-1$? [duplicate]

Why does Wolfram Alpha say that $\sqrt{1}=-1$? Is this a mistake or what? Can anyone help? Thanks in advance.
230 views

### A question about eliminating square roots [duplicate]

If $\sqrt{x^2} = \pm x$, then why does $\sqrt{(x+2)^2} = x+2$ and not $\pm (x+2)$? This is driving me crazy, so feel free to elucidate. Thanks! ---EDIT--- I'm not sure how the other questions' ...
68 views

### Square roots: $-\sqrt{a} = \sqrt{b}$ [duplicate]

[CLOSED] Thanks GoodDeeds and Henry [1] I understood the fundamental problem. As √9 = ± 3 If , √A = √B Thus, ** ±a = ±b** And so a = b; -a = b; and a = -b;; Thus, √9 = +3 OR -3 Let, √A = ±a ...
91 views

### Why does a root only have a positive output? [duplicate]

Let's say I am solving an equation, and end up with this: x^2 = 16 The solutions will be x=4 or x=-4 That makes sense. But when I have this: x = √16 The only solution is x=4 ...
3k views

### Significance of $\sqrt[n]{a^n}$?!

There is a formula given in my module: $$\sqrt[n]{a^n} = \begin{cases} \, a &\text{ if n is odd } \\ |a| &\text{ if n is even } \end{cases}$$ I don't really understand the ...
383 views

### Why does the square root of a square involve the plus-minus sign?

If $\sqrt{x^2}$ can be simplified as follows: $\sqrt{x^2} = (x^2)^\frac{1}{2} = x^{\frac{2}{1}\times\frac{1}{2}} =x^\frac{2}{2} = x^1 = x$ Then why would $\sqrt{x^2} = \pm x$?
48 views

### Definition of “ the principal n-th root of ” using a sign condition.[modified title]

[ Edited] Is it ok to say that, the principal n-th root of a is simply the number x such that : (1) x to the n-th power is equal to a and (2) x has the same sign as a ? My question deals ...